Related papers: Leaves of preferential attachment trees
We propose a model that generates a new class of networks exhibiting power-law degree distribution with a spectrum of exponents depending on the number of links ($m$) with which incoming nodes join the existing network. Unlike the…
This paper analyzes key properties of networks generated by geometric preferential attachment. We establish that the expected number of triangles is proportional to that of the standard preferential attachment model, with a proportionality…
For most networks, the connection between two nodes is the result of their mutual affinity and attachment. In this paper, we propose a mutual selection model to characterize the weighted networks. By introducing a general mechanism of…
We present a process-level Poisson-approximation result for the degree-k vertices in a high-density weighted random connection model with preferential-attachment kernel in the unit volume. Our main focus lies on the impact of the left tails…
We consider the open problem concerning the possible lack of concentration of the degree distribution in preferential attachment graphs with random initial degree, when its distribution is characterized by extremely heavy tails of power-law…
Preferential attachment schemes, where the selection mechanism is linear and possibly time-dependent, are considered, and an infinite-dimensional large deviation principle for the sample path evolution of the empirical degree distribution…
Complex systems can be characterized by classes of equivalency of their elements defined according to system specific rules. We propose a generalized preferential attachment model to describe the class size distribution. The model…
We investigate the joint distribution of nodes of small degrees and the degree profile in preferential dynamic attachment circuits. In particular, we study the joint asymptotic distribution of the number of the nodes of outdegree $0$…
Many important real-world networks manifest "small-world" properties such as scale-free degree distributions, small diameters, and clustering. The most common model of growth for these networks is "preferential attachment", where nodes…
We consider a preferential attachment model that incorporates an anomaly. Our goal is to understand the evolution of the network before and after the occurrence of the anomaly by studying the influence of the anomaly on the structural…
The multiplex network growth literature has been confined to homogeneous growth hitherto, where the number of links that each new incoming node establishes is the same across layers. This paper focuses on heterogeneous growth. We first…
In this paper, we analyze the local clustering coefficient of preferential attachment models. A general approach to preferential attachment was introduced in earlier, where a wide class of models (PA-class) was defined in terms of…
We study a general model of recursive trees where vertices are equipped with independent weights and at each time-step a vertex is sampled with probability proportional to its fitness function (a function of its weight and degree) and…
Preferential attachment is a popular model of growing networks. We consider a generalized model with random node removal, and a combination of preferential and random attachment. Using a high-degree expansion of the master equation, we…
In this paper, we study some important statistics of the random graph in the directed preferential attachment model introduced by B. Bollob\'as, C. Borgs, J. Chayes and O. Riordan. First, we find a new asymptotic formula for the expectation…
Preferential attachment is widely used to model power-law behavior of degree distributions in both directed and undirected networks. Practical analyses on the tail exponent of the power-law degree distribution use the Hill estimator as one…
We investigate the degree sequences of geometric preferential attachment graphs in general compact metric spaces. We show that, under certain conditions on the attractiveness function, the behaviour of the degree sequence is similar to that…
In this paper, we first discuss the origin of preferential attachment. Then we establish the generalized preferential attachment which has two new properties; first, it encapsulates both the topological and weight aspects of a network,…
Preferential attachment, homophily and, their consequences such as the glass ceiling effect have been well-studied in the context of undirected networks. However, the lack of an intuitive, theoretically tractable model of a directed,…
In principle, the rules of links formation of a network model can be considered as a kind of link prediction algorithm. By revisiting the preferential attachment mechanism for generating a scale-free network, here we propose a class of…